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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 05:31:06 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228221124s8la7pqs59rzbhk.htm/, Retrieved Sun, 19 May 2024 12:01:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27680, Retrieved Sun, 19 May 2024 12:01:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F         [Law of Averages] [question 3] [2008-12-02 12:31:06] [f7fbcd402030df685d3fe4ce577d7846] [Current]
Feedback Forum
2008-12-05 13:37:44 [Glenn Maras] [reply] 
Juist, d=1 en D=0. Er kon nog gezegd worden dat de variantie zo klein mogelijk moet zijn omdat het risico, de volatiliteit dan het kleinst is.
2008-12-08 22:04:34 [Gilliam Schoorel] [reply] 
De conclusie klopt, maar er is toch heel weinig uitleg gegeven over de VRM methode.

d = aantal keer gedifferentieerd
D = betrekking op seizoenaal differentieel
In de meest linkse kolom ziet men de bewerkingen die zijn uitgevoerd op de tijdreeks. Hiernaast kan je de variantie zien en aan de rechtse kolom de getrimde variantie.
Je kan zien op de bewerkingen dat de tijdreeks een aantal keren gedifferentieerd is geworden. Bij d = 0 en de D = 0 bekom je een ruwe variantie. Bij de differentiatie d = 1 en de D = 0 bekom je een gewone differentiatie. Wanneer je d = 2 en de D = 0 gebruikt krijg je 2 keer een gewone differentiatie. De variantie van de tijdreeks weerspiegelt het risico of de volatiliteit van/in de tijdreeks. Als je de variantie zo klein mogelijk kan houden kan men meer verklaren over de tijdreeks.

De kleinste variantie staat meestal op dezelfde rij als de kleinste getrimde variantie. Indien dit niet het geval is kan men best opteren voor de de getrimde variabele omdat deze veel betrouwbaarder/geloofwaardiger is.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27680&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27680&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)95.2200400801603Range39Trim Var.68.4660201647041
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)2.05229772207542Range4Trim Var.0
V(Y[t],d=3,D=0)6.12095151554488Range8Trim Var.2.79010520824276
V(Y[t],d=0,D=1)13.4556165213586Range18Trim Var.6.60224062108444
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)4.19792117432438Range8Trim Var.2.30619725708282
V(Y[t],d=3,D=1)12.5867598193746Range16Trim Var.6.48220245406385
V(Y[t],d=0,D=2)22.4939761167625Range24Trim Var.14.0606145676153
V(Y[t],d=1,D=2)6.06664001776593Range8Trim Var.2.58297720797721
V(Y[t],d=2,D=2)13.0570824524313Range16Trim Var.6.89131915440468
V(Y[t],d=3,D=2)39.1947540043717Range32Trim Var.21.3403541637659

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 95.2200400801603 & Range & 39 & Trim Var. & 68.4660201647041 \tabularnewline
V(Y[t],d=1,D=0) & 0.99862375353116 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.05229772207542 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.12095151554488 & Range & 8 & Trim Var. & 2.79010520824276 \tabularnewline
V(Y[t],d=0,D=1) & 13.4556165213586 & Range & 18 & Trim Var. & 6.60224062108444 \tabularnewline
V(Y[t],d=1,D=1) & 1.98352219433670 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.19792117432438 & Range & 8 & Trim Var. & 2.30619725708282 \tabularnewline
V(Y[t],d=3,D=1) & 12.5867598193746 & Range & 16 & Trim Var. & 6.48220245406385 \tabularnewline
V(Y[t],d=0,D=2) & 22.4939761167625 & Range & 24 & Trim Var. & 14.0606145676153 \tabularnewline
V(Y[t],d=1,D=2) & 6.06664001776593 & Range & 8 & Trim Var. & 2.58297720797721 \tabularnewline
V(Y[t],d=2,D=2) & 13.0570824524313 & Range & 16 & Trim Var. & 6.89131915440468 \tabularnewline
V(Y[t],d=3,D=2) & 39.1947540043717 & Range & 32 & Trim Var. & 21.3403541637659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27680&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]95.2200400801603[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]68.4660201647041[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99862375353116[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2.05229772207542[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6.12095151554488[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.79010520824276[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.4556165213586[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.60224062108444[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.98352219433670[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4.19792117432438[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.30619725708282[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.5867598193746[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.48220245406385[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]22.4939761167625[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]14.0606145676153[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.06664001776593[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.58297720797721[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.0570824524313[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.89131915440468[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.1947540043717[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.3403541637659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27680&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)95.2200400801603Range39Trim Var.68.4660201647041
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)2.05229772207542Range4Trim Var.0
V(Y[t],d=3,D=0)6.12095151554488Range8Trim Var.2.79010520824276
V(Y[t],d=0,D=1)13.4556165213586Range18Trim Var.6.60224062108444
V(Y[t],d=1,D=1)1.98352219433670Range4Trim Var.0
V(Y[t],d=2,D=1)4.19792117432438Range8Trim Var.2.30619725708282
V(Y[t],d=3,D=1)12.5867598193746Range16Trim Var.6.48220245406385
V(Y[t],d=0,D=2)22.4939761167625Range24Trim Var.14.0606145676153
V(Y[t],d=1,D=2)6.06664001776593Range8Trim Var.2.58297720797721
V(Y[t],d=2,D=2)13.0570824524313Range16Trim Var.6.89131915440468
V(Y[t],d=3,D=2)39.1947540043717Range32Trim Var.21.3403541637659


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(x,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')